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The Trotter-Kato theorem and approximation of PDEs

Authors: Kazufumi Ito and Franz Kappel
Journal: Math. Comp. 67 (1998), 21-44
MSC (1991): Primary 47D05, 47H05, 65J10, 35K22, 35L99
MathSciNet review: 1443120
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Abstract: We present formulations of the Trotter-Kato theorem for approximation of linear C${}_0$-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.

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Additional Information

Kazufumi Ito
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695

Franz Kappel
Affiliation: Institut für Mathematik, Universität Graz, Heinrichstraße 36, A8010 Graz, Austria

Keywords: Semigroups of transformations, Trotter-Kato-Theorems, numerical approximation of linear evolutionary equations
Received by editor(s): August 18, 1995
Received by editor(s) in revised form: August 1, 1996
Additional Notes: Research of the first author was supported in part by the NSF under Grant UINT-8521208 and DMS-8818530 and by the Air Force Office of Scientific Research under contract AFOSR-90-0091.
Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146-PHY and under F003.
Article copyright: © Copyright 1998 American Mathematical Society